2005_Solutions_Grades 5-6-2005_Solutions_Levels

2005_Solutions_Levels_5&6
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The Math Kangaroo 2005 competition provides a set of math questions for students to solve, with solutions that demonstrate various problem-solving techniques. Below is a brief summary of some solutions provided:<br /><br />1. <strong>Butterfly Problem (Solution: E)</strong>: Calculating the remaining distance after subtractions gives 1290.<br /><br />2. <strong>Candy Distribution (Solution: C)</strong>: Determines that Olla has 6 pieces of candy when Anna gets an equal share.<br /><br />3. <strong>Kangaroo Arrangement (Solution: B)</strong>: Reorganizing kangaroos gives one in each necessary row and column.<br /><br />4. <strong>Animal and Leg Count (Solution: D)</strong>: Summing legs from animals and people totals 24.<br /><br />5. <strong>Arithmetic Manipulation (Solution: D)</strong>: Breaking down and combining moves results in the number 202505.<br /><br />6. <strong>Ant's Path (Solution: D)</strong>: The calculated ant path totals 60 cm.<br /><br />7. <strong>Marble Colors (Solution: D)</strong>: Determining non-white marbles leaves 7 brown marbles.<br /><br />8. <strong>Card Moves (Solution: A)</strong>: Switching positions in two moves arranges cards correctly.<br /><br />9. <strong>Multiples of Three (Solution: E)</strong>: Identifies 103 as not derived from multiplying three.<br /><br />10. <strong>Time Calculation (Solution: C)</strong>: A breakdown of an hour calculated from a day fraction.<br /><br />11. <strong>Napkin Cuts (Solution: C)</strong>: Systematic cutting results in 37 pieces.<br /><br />12. <strong>Mowgli's Travel Time (Solution: D)</strong>: Total foot travel calculated at 48 minutes.<br /><br />13. <strong>Garden Area (Solution: C)</strong>: Rectangular area is calculated to 8 m².<br /><br />14. <strong>Peanut Distribution (Solution: E)</strong>: 7 members get more than grandpa's distribution.<br /><br />15. <strong>Odd Digit Numbers (Solution: B)</strong>: Combinatorial counting results in 20 possible combinations.<br /><br />16. <strong>Cube Configuration (Solution: B)</strong>: Consistent characteristics identify a particular option.<br /><br />17. <strong>Middle Number Formula (Solution: B)</strong>: 403 as the largest of five numbers.<br /><br />18. <strong>Divisors of 100 (Solution: E)</strong>: Lists 9 unique divisors.<br /><br />19. <strong>Frame Width (Solution: C)</strong>: Calculated using the perimeter difference, yielding 1 decimeter width.<br /><br />20. <strong>Shape Puzzle (Solution: E)</strong>: There are 10 triangles, 3 more than squares.<br /><br />21. <strong>Chest Unlocking (Solution: E)</strong>: 8 lock openings yield 50 coins.<br /><br />22. <strong>Sequential Operations (Solution: D)</strong>: Summation to arrive at 82.<br /><br />23. <strong>Number Multiples (Solution: D)</strong>: Finding consistent conditions where a number is a multiple of six.<br /><br />24. <strong>Paint Consumption (Solution: D)</strong>: Unpainted cubes require 0.5 gallons more paint.<br /><br />25. <strong>Area Ratios (Solution: D)</strong>: Ratio of shaded versus unshaded parts is 2:3.<br /><br />26. <strong>Watch Note Validity (Solution: C)</strong>: 18 hours where the note applies.<br /><br />27. <strong>Prism Dimensions (Solution: D)</strong>: Data shows height must be 3 cm.<br /><br />28. <strong>Perfect Square Options (Solution: D)</strong>: Logical deduction of possible digit setups results in 421, 463, 931, 962.<br /><br />29. <strong>Shaded Triangular Area (Solution: B)</strong>: Shaded region calculates to an equivalent of 22.5 triangle areas.<br /><br />30. <strong>Seating Arrangement (Solution: D)</strong>: Deduction leads to Ella sitting farthest to the right.<br /><br />This compilation showcases an array of problem-solving skills necessary for a math competition setup. Each question requires analytical and deductive reasoning across various mathematical topics.
Keywords
Math Kangaroo 2005
math competition
problem-solving techniques
math questions
solutions
analytical reasoning
deductive reasoning
mathematical topics
student competition
math skills